Computation of power system load flows and transient stability

ABSTRACT

A loadflow calculator having transient stability analysis capability includes a plurality of operational amplifier DC circuits for simulation of an electric power system. The calculator responds to signals representative of predetermined network variables to produce output signals representative of AC network parameters to attain loadflow solutions and provide signal parameters for transient stability studies after one or more transient faults have been imposed on the D.C. circuits.

United States Patent [191 Carlson et al.

[111 3,832,534 Aug. 27, 1974 COMPUTATION OF POWER SYSTEM LOAD FLOWS AND TRANSIENT STABILITY [75] Inventors: Norman R. Carlson, Export;

William E. Zitelli, Pittsburgh; Victor Burtnyk, Monroeville, all of Pa. [73] Assignee: Westinghouse Electric Corporation,

Pittsburgh, Pa. [22] Filed: May 19, 1972 [21] Appl. No.: 255,167

[52] US. Cl 235/151.21, 444/1, 340/1725 [51] Int. Cl...... G06j 1/00, G06f 15/06, G06f 15/56 [58] Field of Search 235/15l.21, 150.5, 150, 235/151.l, 184; 307/18, 19, 20, 24, 30, 31, 52, 62; 444/1; 340/1725 [56] References Cited UNITED STATES PATENTS 3,341,697 9/1967 Kaufman et al. 235/1505 X 3,582,628 6/1971 Brussolo 235/1505 3,675,002 7/1972 Mitsui et al.... 235/184 X 3,699,538 10/1972 Van Essen..... 340/1725 X 3,701,891 10/1972 Cohn 235/184 X OTHER PUBLICATIONS Load Flows by Hybrid Computation for Power System Operations; M. Enns, T. C. Giras, & N. R. Carlson; IEEE Transactions on Power Apparatus and Systems, Nov./Dec. 1971, pp. 2540-2547.

Techniques for the Real-Time Monitoring of Power System Operations; G. W. Stagg, J. F. Dopazo, O. A. Klitin, & L. S. Vanslyck; IEEE Transactions on Power Apparatus and Systems; Vol. PAS-89, No. 4, April 1970, pp. 545-555.

Load Flows Using A Combination of Point Jacobi and Newtons Methods; Y. P. Dusonchet, S. N. Talukdar, H. E. Sinnot; IEEE Transactions on Power Apparatus and Systems; Vol. PAS-90, No. 3, May/June 1971, pp. 941-949.

Computer Control of Power Systems, The Engineer, Oct. 2, 1964.

Primary Examiner-Malcolm A. Morrison Assistant Examiner-Edward J. Wise Attorney, Agent, or FirmE. F. Possessky ABSTRACT 6 Claims, 41 Drawing Figures NORTH r' 13 II g EHV(5OOKV so) -4 5 (jasLOAD 3 I34 3% PHILADELPHIA 20 L21 12 156 2 3 47 EHV BUFFALO 25 D LOA WASHINGTON r 22 MLAM 196 WHEEVLING 9 WEST LOAD

PAIENTEBMIBZTW I I 3.882.534

SHEET 01 If 23 NORTH v r' III II EHV(5OOKV-3I -4 5 a E5LOAD 3 I34 PHILADELPHIA {20 ZI 2 56 2 3 47' EHV BUFFALO 26 LOAD EHV WASHINGTON 8 MAJ- AA; f /96 WW WHEELING WEST 28 LOAD FIG.I

INJECTION CURRENT VALVES 4A 4l- W 0 TRANSMISSION NETWORK SIMULATOR Lemmas u Tm; V vs LINES ausss GENERATION a SVQI s rams-"omens FIG.2 I

PATENTEWZY'Q" 3.882.534

SHEET 02 0f 23 BUS F 308 I 3w 1,: 2 e INTEGRATOR v Ep [35. 320 L ADMITTANCE I LINE (p-q) I323 ADMITTANCE \l YPI' EHiEw-n) i n l v I l v I325 r324 FIGB ADMITTANCE Y n \l p 1E" Foe LLINE (p-n) LINE OUTAGE SWITCHING AN LO DIGITAL A GENERATION Argfigoe COMPUTER POWER gig AND LINE VOLTAGE MODULES [E] MODULES SET POINTS I J BUS VOLTAGES AND LINE CURRENT SOLUTION FIGI4 6| Pps so P 5- ILL 2 S r EP Pp [9+ TO BUS-P 73 2 r ED) E 1 74 5' Ie gI B] ATENTED M182 7 1974 3.832. 534

sum 03 or 23 FIG? PATENTEDAUBNISH 3, 32,53

SHEET '05 or 23 LINE OUTAGE SWITCHING A/D BUS VOLTAGE AND LINE cuRRENT SOLUTIONS lo I 4 I 413 4|2 V I D/A ANALOG [E] ANALOG [E] DIGITAL POWER DYNAMIC Bus ANALOG COMPUTER VOLTAGE GENERATOR LINE 4 LOADS 'SET POINTS MODULES [1G] MODULES I [IT] SWING ANGLES [E] I RoTATIoNAL vELoITIEs 4|4 D/A INFINITE BUS VOLTAGE Tfiz A'rq SET POINTS INFINITE BUSES Dcu's FORLOAD ADMITTANCE ADJUSTMENTS FIG. IO

LINE CURRENT AND lBUSVOLTAGE soLuTIoNs [4 D/A [1e] U DIGITAL COMPUTER LINE OUTAGE tai 3 SWITCHING 0 8 [1L] ANALOG TIESAND INFINITE BUSES FIG II DCU'S LOAD ADMITTANCE ADJUSTMENT FAULTING I FAULTING DEVICE PATENTEB N162 sum as or 23 w w 3 3 w l 4 i E H A i- .lwn

FAIENIEDmszmn sum 1- a;

PAIENIEBAUB27197-4 3, mf534 2 sum as as 23 REAL BUS FIG. I5A.

VOLT INPUT IMAGINARY BUS VOLT INPUT PArimmuszmu 3,832,534

sum '09 or 23 PATfiminaucznaz-a sum 10 0F 2 ALI I AL2 V AL4 ALB ALI4 ALIZ FIG. ITB

PATENTEDAUBZTW I 3.832.584 sum 12 or 23 INTRONICS MULTIPLIER INTRONICS MULTIPLIER PATENIEDMIBZTIQH 3.832.534

sum 5130f. 23

405 An 7H l -1 :/1|4 M75 K107 I SIGNAL GENERATOR LINE PQ o BUS O G o BUS P 4 LINE GENERATOR BUS LOAD BUS FIG. 20

PATENTED I 3.882.534

sum 15 or 23 D/A INE Bus VOLTAGES O/A IEI, M 7 GENERATOR SET POINTS I MODELS LINE [16] T] OATA SWH-CHING V TRANSFORMER SSSMNK' A/O ANALOG NET I H EL SIMULATOR SOLUTION [E] 982 l LOAD ADMlTT. LOAD SETTINGS MODELS sae 9a1 SYSTEM STUDY OPERATORS MODE FIG.24 

1. A DC loadflow calculator having transient stability analysis capability for simulation of an AC network and including in combination a plurality of D.C. circuits interconnected to correspond to the AC network, at least some of said DC circuits including operational amplifiers for signals representative of predetermined network variables and providing output signals representative of predetermined AC network parameters, means for applying said signals representative of predetermined network variables to said DC circuits of said simulator, means for imposing transient faults on said DC circuits, means for imposing out of service conditions on preselected circuits, and means for displaying steady state and transient network responses from said DC circuits.
 2. A DC calculator as set forth in claim 1 wherein means are provided for generating transient fault signals for application to said transient fault imposing means so as to provide preselected transient fault signals to preselected DC circuits.
 3. A DC calculator as set forth in claim 1 wherein said plurality of DC circuits comprises a plurality of bus, generator, load, line and tie line DC circuits interconnected to correspond to said AC network.
 4. A DC calculator as set forth in claim 3 wherein each of said bus DC circuits includes means for responding to generator, load, tie line and line phasor input current signals and for generating an output bus voltage phasor signal, each of said generator DC circuits includes means for responding to the difference between applied generator mechanical power signals and generator electrical power signals and the difference between applied generator terminal voltage signals and bus voltage phasor signals, and for generating a generaTor swing angle output signal and an output generator current signal, each of said load DC circuits includes means for responding to applied bus voltage phasor signals, means for representing applied first and second load admittance value signals, and means for generating an output bus to load current phasor signal, and each of said tie line and line DC circuits includes means for responding to the difference between applied bus voltage phasor signals and generating an output line phasor current signal in accordance with at least a representation of the equivalent series branch impedance, at least one of said applied bus voltage phasor signals to each of said tie line DC circuits being an infinite bus voltage phasor signal.
 5. A DC calculator as set forth in claim 4 wherein said means for applying signals representative of predetermined network variables includes means for applying and adjusting said generator mechanical power input signals to each of said generator DC circuits, means for applying and adjusting generator voltage magnitude input signals to each of said generator DC circuits, and means for applying and adjusting said first and second load admittance value signals to each of said load DC circuits.
 6. A DC calculator as set forth in claim 4 wherein means are provided for generating transient fault signals for application to said transient fault imposing means so as to provide three phase fault signals to said bus, tie generator, load, tie line and line DC circuits, and swing angle restoration signals and damping signals to said generator DC circuits. 